# Properties

 Label 882.4.g.bi.361.1 Level $882$ Weight $4$ Character 882.361 Analytic conductor $52.040$ Analytic rank $0$ Dimension $4$ CM no Inner twists $4$

# Related objects

## Newspace parameters

 Level: $$N$$ $$=$$ $$882 = 2 \cdot 3^{2} \cdot 7^{2}$$ Weight: $$k$$ $$=$$ $$4$$ Character orbit: $$[\chi]$$ $$=$$ 882.g (of order $$3$$, degree $$2$$, not minimal)

## Newform invariants

 Self dual: no Analytic conductor: $$52.0396846251$$ Analytic rank: $$0$$ Dimension: $$4$$ Relative dimension: $$2$$ over $$\Q(\zeta_{3})$$ Coefficient field: $$\Q(\sqrt{-3}, \sqrt{22})$$ Defining polynomial: $$x^{4} + 22 x^{2} + 484$$ Coefficient ring: $$\Z[a_1, \ldots, a_{25}]$$ Coefficient ring index: $$2^{2}$$ Twist minimal: no (minimal twist has level 98) Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

## Embedding invariants

 Embedding label 361.1 Root $$-2.34521 - 4.06202i$$ of defining polynomial Character $$\chi$$ $$=$$ 882.361 Dual form 882.4.g.bi.667.1

## $q$-expansion

 $$f(q)$$ $$=$$ $$q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-4.69042 - 8.12404i) q^{5} -8.00000 q^{8} +O(q^{10})$$ $$q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-4.69042 - 8.12404i) q^{5} -8.00000 q^{8} +(9.38083 - 16.2481i) q^{10} +(10.0000 - 17.3205i) q^{11} -65.6658 q^{13} +(-8.00000 - 13.8564i) q^{16} +(-28.1425 + 48.7442i) q^{17} +(4.69042 + 8.12404i) q^{19} +37.5233 q^{20} +40.0000 q^{22} +(24.0000 + 41.5692i) q^{23} +(18.5000 - 32.0429i) q^{25} +(-65.6658 - 113.737i) q^{26} +166.000 q^{29} +(-103.189 + 178.729i) q^{31} +(16.0000 - 27.7128i) q^{32} -112.570 q^{34} +(39.0000 + 67.5500i) q^{37} +(-9.38083 + 16.2481i) q^{38} +(37.5233 + 64.9923i) q^{40} +393.995 q^{41} +436.000 q^{43} +(40.0000 + 69.2820i) q^{44} +(-48.0000 + 83.1384i) q^{46} +(-103.189 - 178.729i) q^{47} +74.0000 q^{50} +(131.332 - 227.473i) q^{52} +(31.0000 - 53.6936i) q^{53} -187.617 q^{55} +(166.000 + 287.520i) q^{58} +(333.020 - 576.807i) q^{59} +(136.022 + 235.597i) q^{61} -412.757 q^{62} +64.0000 q^{64} +(308.000 + 533.472i) q^{65} +(-290.000 + 502.295i) q^{67} +(-112.570 - 194.977i) q^{68} +544.000 q^{71} +(-300.187 + 519.938i) q^{73} +(-78.0000 + 135.100i) q^{74} -37.5233 q^{76} +(340.000 + 588.897i) q^{79} +(-75.0467 + 129.985i) q^{80} +(393.995 + 682.419i) q^{82} +196.997 q^{83} +528.000 q^{85} +(436.000 + 755.174i) q^{86} +(-80.0000 + 138.564i) q^{88} +(750.467 + 1299.85i) q^{89} -192.000 q^{92} +(206.378 - 357.458i) q^{94} +(44.0000 - 76.2102i) q^{95} +656.658 q^{97} +O(q^{100})$$ $$\operatorname{Tr}(f)(q)$$ $$=$$ $$4q + 4q^{2} - 8q^{4} - 32q^{8} + O(q^{10})$$ $$4q + 4q^{2} - 8q^{4} - 32q^{8} + 40q^{11} - 32q^{16} + 160q^{22} + 96q^{23} + 74q^{25} + 664q^{29} + 64q^{32} + 156q^{37} + 1744q^{43} + 160q^{44} - 192q^{46} + 296q^{50} + 124q^{53} + 664q^{58} + 256q^{64} + 1232q^{65} - 1160q^{67} + 2176q^{71} - 312q^{74} + 1360q^{79} + 2112q^{85} + 1744q^{86} - 320q^{88} - 768q^{92} + 176q^{95} + O(q^{100})$$

## Character values

We give the values of $$\chi$$ on generators for $$\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$$.

 $$n$$ $$199$$ $$785$$ $$\chi(n)$$ $$e\left(\frac{2}{3}\right)$$ $$1$$

## Coefficient data

For each $$n$$ we display the coefficients of the $$q$$-expansion $$a_n$$, the Satake parameters $$\alpha_p$$, and the Satake angles $$\theta_p = \textrm{Arg}(\alpha_p)$$.

Display $$a_p$$ with $$p$$ up to: 50 250 1000 Display $$a_n$$ with $$n$$ up to: 50 250 1000
$$n$$ $$a_n$$ $$a_n / n^{(k-1)/2}$$ $$\alpha_n$$ $$\theta_n$$
$$p$$ $$a_p$$ $$a_p / p^{(k-1)/2}$$ $$\alpha_p$$ $$\theta_p$$
$$2$$ 1.00000 + 1.73205i 0.353553 + 0.612372i
$$3$$ 0 0
$$4$$ −2.00000 + 3.46410i −0.250000 + 0.433013i
$$5$$ −4.69042 8.12404i −0.419524 0.726636i 0.576368 0.817190i $$-0.304470\pi$$
−0.995892 + 0.0905542i $$0.971136\pi$$
$$6$$ 0 0
$$7$$ 0 0
$$8$$ −8.00000 −0.353553
$$9$$ 0 0
$$10$$ 9.38083 16.2481i 0.296648 0.513809i
$$11$$ 10.0000 17.3205i 0.274101 0.474757i −0.695807 0.718229i $$-0.744953\pi$$
0.969908 + 0.243472i $$0.0782863\pi$$
$$12$$ 0 0
$$13$$ −65.6658 −1.40096 −0.700478 0.713674i $$-0.747030\pi$$
−0.700478 + 0.713674i $$0.747030\pi$$
$$14$$ 0 0
$$15$$ 0 0
$$16$$ −8.00000 13.8564i −0.125000 0.216506i
$$17$$ −28.1425 + 48.7442i −0.401503 + 0.695424i −0.993908 0.110217i $$-0.964846\pi$$
0.592404 + 0.805641i $$0.298179\pi$$
$$18$$ 0 0
$$19$$ 4.69042 + 8.12404i 0.0566345 + 0.0980938i 0.892953 0.450151i $$-0.148630\pi$$
−0.836318 + 0.548244i $$0.815296\pi$$
$$20$$ 37.5233 0.419524
$$21$$ 0 0
$$22$$ 40.0000 0.387638
$$23$$ 24.0000 + 41.5692i 0.217580 + 0.376860i 0.954068 0.299591i $$-0.0968503\pi$$
−0.736487 + 0.676451i $$0.763517\pi$$
$$24$$ 0 0
$$25$$ 18.5000 32.0429i 0.148000 0.256344i
$$26$$ −65.6658 113.737i −0.495313 0.857907i
$$27$$ 0 0
$$28$$ 0 0
$$29$$ 166.000 1.06295 0.531473 0.847075i $$-0.321639\pi$$
0.531473 + 0.847075i $$0.321639\pi$$
$$30$$ 0 0
$$31$$ −103.189 + 178.729i −0.597849 + 1.03550i 0.395289 + 0.918557i $$0.370644\pi$$
−0.993138 + 0.116948i $$0.962689\pi$$
$$32$$ 16.0000 27.7128i 0.0883883 0.153093i
$$33$$ 0 0
$$34$$ −112.570 −0.567812
$$35$$ 0 0
$$36$$ 0 0
$$37$$ 39.0000 + 67.5500i 0.173285 + 0.300139i 0.939567 0.342366i $$-0.111228\pi$$
−0.766281 + 0.642505i $$0.777895\pi$$
$$38$$ −9.38083 + 16.2481i −0.0400466 + 0.0693628i
$$39$$ 0 0
$$40$$ 37.5233 + 64.9923i 0.148324 + 0.256905i
$$41$$ 393.995 1.50077 0.750386 0.661000i $$-0.229868\pi$$
0.750386 + 0.661000i $$0.229868\pi$$
$$42$$ 0 0
$$43$$ 436.000 1.54626 0.773132 0.634245i $$-0.218689\pi$$
0.773132 + 0.634245i $$0.218689\pi$$
$$44$$ 40.0000 + 69.2820i 0.137051 + 0.237379i
$$45$$ 0 0
$$46$$ −48.0000 + 83.1384i −0.153852 + 0.266480i
$$47$$ −103.189 178.729i −0.320249 0.554687i 0.660291 0.751010i $$-0.270433\pi$$
−0.980539 + 0.196323i $$0.937100\pi$$
$$48$$ 0 0
$$49$$ 0 0
$$50$$ 74.0000 0.209304
$$51$$ 0 0
$$52$$ 131.332 227.473i 0.350239 0.606632i
$$53$$ 31.0000 53.6936i 0.0803430 0.139158i −0.823054 0.567963i $$-0.807732\pi$$
0.903397 + 0.428805i $$0.141065\pi$$
$$54$$ 0 0
$$55$$ −187.617 −0.459968
$$56$$ 0 0
$$57$$ 0 0
$$58$$ 166.000 + 287.520i 0.375808 + 0.650919i
$$59$$ 333.020 576.807i 0.734838 1.27278i −0.219956 0.975510i $$-0.570591\pi$$
0.954794 0.297267i $$-0.0960752\pi$$
$$60$$ 0 0
$$61$$ 136.022 + 235.597i 0.285506 + 0.494510i 0.972732 0.231933i $$-0.0745052\pi$$
−0.687226 + 0.726444i $$0.741172\pi$$
$$62$$ −412.757 −0.845486
$$63$$ 0 0
$$64$$ 64.0000 0.125000
$$65$$ 308.000 + 533.472i 0.587734 + 1.01798i
$$66$$ 0 0
$$67$$ −290.000 + 502.295i −0.528793 + 0.915897i 0.470643 + 0.882324i $$0.344022\pi$$
−0.999436 + 0.0335729i $$0.989311\pi$$
$$68$$ −112.570 194.977i −0.200752 0.347712i
$$69$$ 0 0
$$70$$ 0 0
$$71$$ 544.000 0.909309 0.454654 0.890668i $$-0.349763\pi$$
0.454654 + 0.890668i $$0.349763\pi$$
$$72$$ 0 0
$$73$$ −300.187 + 519.938i −0.481290 + 0.833619i −0.999769 0.0214711i $$-0.993165\pi$$
0.518479 + 0.855090i $$0.326498\pi$$
$$74$$ −78.0000 + 135.100i −0.122531 + 0.212230i
$$75$$ 0 0
$$76$$ −37.5233 −0.0566345
$$77$$ 0 0
$$78$$ 0 0
$$79$$ 340.000 + 588.897i 0.484215 + 0.838685i 0.999836 0.0181320i $$-0.00577190\pi$$
−0.515621 + 0.856817i $$0.672439\pi$$
$$80$$ −75.0467 + 129.985i −0.104881 + 0.181659i
$$81$$ 0 0
$$82$$ 393.995 + 682.419i 0.530603 + 0.919032i
$$83$$ 196.997 0.260521 0.130261 0.991480i $$-0.458419\pi$$
0.130261 + 0.991480i $$0.458419\pi$$
$$84$$ 0 0
$$85$$ 528.000 0.673760
$$86$$ 436.000 + 755.174i 0.546687 + 0.946890i
$$87$$ 0 0
$$88$$ −80.0000 + 138.564i −0.0969094 + 0.167852i
$$89$$ 750.467 + 1299.85i 0.893812 + 1.54813i 0.835268 + 0.549843i $$0.185313\pi$$
0.0585446 + 0.998285i $$0.481354\pi$$
$$90$$ 0 0
$$91$$ 0 0
$$92$$ −192.000 −0.217580
$$93$$ 0 0
$$94$$ 206.378 357.458i 0.226450 0.392223i
$$95$$ 44.0000 76.2102i 0.0475190 0.0823053i
$$96$$ 0 0
$$97$$ 656.658 0.687356 0.343678 0.939088i $$-0.388327\pi$$
0.343678 + 0.939088i $$0.388327\pi$$
$$98$$ 0 0
$$99$$ 0 0
$$100$$ 74.0000 + 128.172i 0.0740000 + 0.128172i
$$101$$ −60.9754 + 105.612i −0.0600721 + 0.104048i −0.894497 0.447073i $$-0.852466\pi$$
0.834425 + 0.551121i $$0.185800\pi$$
$$102$$ 0 0
$$103$$ −684.801 1186.11i −0.655101 1.13467i −0.981868 0.189564i $$-0.939293\pi$$
0.326767 0.945105i $$-0.394041\pi$$
$$104$$ 525.327 0.495313
$$105$$ 0 0
$$106$$ 124.000 0.113622
$$107$$ −130.000 225.167i −0.117454 0.203436i 0.801304 0.598257i $$-0.204140\pi$$
−0.918758 + 0.394821i $$0.870807\pi$$
$$108$$ 0 0
$$109$$ −941.000 + 1629.86i −0.826894 + 1.43222i 0.0735690 + 0.997290i $$0.476561\pi$$
−0.900463 + 0.434932i $$0.856772\pi$$
$$110$$ −187.617 324.962i −0.162623 0.281672i
$$111$$ 0 0
$$112$$ 0 0
$$113$$ 1286.00 1.07059 0.535295 0.844665i $$-0.320200\pi$$
0.535295 + 0.844665i $$0.320200\pi$$
$$114$$ 0 0
$$115$$ 225.140 389.954i 0.182560 0.316203i
$$116$$ −332.000 + 575.041i −0.265736 + 0.460269i
$$117$$ 0 0
$$118$$ 1332.08 1.03922
$$119$$ 0 0
$$120$$ 0 0
$$121$$ 465.500 + 806.270i 0.349737 + 0.605762i
$$122$$ −272.044 + 471.194i −0.201883 + 0.349671i
$$123$$ 0 0
$$124$$ −412.757 714.915i −0.298924 0.517752i
$$125$$ −1519.69 −1.08741
$$126$$ 0 0
$$127$$ 2312.00 1.61541 0.807704 0.589588i $$-0.200710\pi$$
0.807704 + 0.589588i $$0.200710\pi$$
$$128$$ 64.0000 + 110.851i 0.0441942 + 0.0765466i
$$129$$ 0 0
$$130$$ −616.000 + 1066.94i −0.415591 + 0.719824i
$$131$$ 126.641 + 219.349i 0.0844633 + 0.146295i 0.905162 0.425066i $$-0.139749\pi$$
−0.820699 + 0.571361i $$0.806416\pi$$
$$132$$ 0 0
$$133$$ 0 0
$$134$$ −1160.00 −0.747826
$$135$$ 0 0
$$136$$ 225.140 389.954i 0.141953 0.245870i
$$137$$ −557.000 + 964.752i −0.347356 + 0.601638i −0.985779 0.168048i $$-0.946254\pi$$
0.638423 + 0.769686i $$0.279587\pi$$
$$138$$ 0 0
$$139$$ −1378.98 −0.841466 −0.420733 0.907185i $$-0.638227\pi$$
−0.420733 + 0.907185i $$0.638227\pi$$
$$140$$ 0 0
$$141$$ 0 0
$$142$$ 544.000 + 942.236i 0.321489 + 0.556836i
$$143$$ −656.658 + 1137.37i −0.384004 + 0.665114i
$$144$$ 0 0
$$145$$ −778.609 1348.59i −0.445931 0.772375i
$$146$$ −1200.75 −0.680647
$$147$$ 0 0
$$148$$ −312.000 −0.173285
$$149$$ −473.000 819.260i −0.260065 0.450446i 0.706194 0.708018i $$-0.250411\pi$$
−0.966259 + 0.257573i $$0.917077\pi$$
$$150$$ 0 0
$$151$$ −416.000 + 720.533i −0.224196 + 0.388319i −0.956078 0.293113i $$-0.905309\pi$$
0.731882 + 0.681431i $$0.238642\pi$$
$$152$$ −37.5233 64.9923i −0.0200233 0.0346814i
$$153$$ 0 0
$$154$$ 0 0
$$155$$ 1936.00 1.00325
$$156$$ 0 0
$$157$$ 1439.96 2494.08i 0.731982 1.26783i −0.224053 0.974577i $$-0.571929\pi$$
0.956035 0.293253i $$-0.0947377\pi$$
$$158$$ −680.000 + 1177.79i −0.342392 + 0.593040i
$$159$$ 0 0
$$160$$ −300.187 −0.148324
$$161$$ 0 0
$$162$$ 0 0
$$163$$ −318.000 550.792i −0.152808 0.264671i 0.779451 0.626463i $$-0.215498\pi$$
−0.932259 + 0.361792i $$0.882165\pi$$
$$164$$ −787.990 + 1364.84i −0.375193 + 0.649854i
$$165$$ 0 0
$$166$$ 196.997 + 341.210i 0.0921082 + 0.159536i
$$167$$ −656.658 −0.304274 −0.152137 0.988359i $$-0.548615\pi$$
−0.152137 + 0.988359i $$0.548615\pi$$
$$168$$ 0 0
$$169$$ 2115.00 0.962676
$$170$$ 528.000 + 914.523i 0.238210 + 0.412592i
$$171$$ 0 0
$$172$$ −872.000 + 1510.35i −0.386566 + 0.669552i
$$173$$ −333.020 576.807i −0.146353 0.253490i 0.783524 0.621361i $$-0.213420\pi$$
−0.929877 + 0.367871i $$0.880087\pi$$
$$174$$ 0 0
$$175$$ 0 0
$$176$$ −320.000 −0.137051
$$177$$ 0 0
$$178$$ −1500.93 + 2599.69i −0.632021 + 1.09469i
$$179$$ −1614.00 + 2795.53i −0.673944 + 1.16731i 0.302832 + 0.953044i $$0.402068\pi$$
−0.976776 + 0.214262i $$0.931265\pi$$
$$180$$ 0 0
$$181$$ 2823.63 1.15955 0.579776 0.814776i $$-0.303140\pi$$
0.579776 + 0.814776i $$0.303140\pi$$
$$182$$ 0 0
$$183$$ 0 0
$$184$$ −192.000 332.554i −0.0769262 0.133240i
$$185$$ 365.852 633.675i 0.145395 0.251831i
$$186$$ 0 0
$$187$$ 562.850 + 974.885i 0.220105 + 0.381233i
$$188$$ 825.513 0.320249
$$189$$ 0 0
$$190$$ 176.000 0.0672020
$$191$$ −1068.00 1849.83i −0.404596 0.700780i 0.589679 0.807638i $$-0.299254\pi$$
−0.994274 + 0.106858i $$0.965921\pi$$
$$192$$ 0 0
$$193$$ −829.000 + 1435.87i −0.309185 + 0.535524i −0.978184 0.207739i $$-0.933390\pi$$
0.668999 + 0.743263i $$0.266723\pi$$
$$194$$ 656.658 + 1137.37i 0.243017 + 0.420918i
$$195$$ 0 0
$$196$$ 0 0
$$197$$ 978.000 0.353704 0.176852 0.984237i $$-0.443409\pi$$
0.176852 + 0.984237i $$0.443409\pi$$
$$198$$ 0 0
$$199$$ −2467.16 + 4273.24i −0.878855 + 1.52222i −0.0262574 + 0.999655i $$0.508359\pi$$
−0.852598 + 0.522567i $$0.824974\pi$$
$$200$$ −148.000 + 256.344i −0.0523259 + 0.0906311i
$$201$$ 0 0
$$202$$ −243.902 −0.0849547
$$203$$ 0 0
$$204$$ 0 0
$$205$$ −1848.00 3200.83i −0.629609 1.09052i
$$206$$ 1369.60 2372.22i 0.463226 0.802332i
$$207$$ 0 0
$$208$$ 525.327 + 909.892i 0.175119 + 0.303316i
$$209$$ 187.617 0.0620943
$$210$$ 0 0
$$211$$ 1556.00 0.507675 0.253838 0.967247i $$-0.418307\pi$$
0.253838 + 0.967247i $$0.418307\pi$$
$$212$$ 124.000 + 214.774i 0.0401715 + 0.0695791i
$$213$$ 0 0
$$214$$ 260.000 450.333i 0.0830525 0.143851i
$$215$$ −2045.02 3542.08i −0.648694 1.12357i
$$216$$ 0 0
$$217$$ 0 0
$$218$$ −3764.00 −1.16940
$$219$$ 0 0
$$220$$ 375.233 649.923i 0.114992 0.199172i
$$221$$ 1848.00 3200.83i 0.562488 0.974258i
$$222$$ 0 0
$$223$$ −2889.30 −0.867630 −0.433815 0.901002i $$-0.642833\pi$$
−0.433815 + 0.901002i $$0.642833\pi$$
$$224$$ 0 0
$$225$$ 0 0
$$226$$ 1286.00 + 2227.42i 0.378511 + 0.655600i
$$227$$ 989.678 1714.17i 0.289371 0.501205i −0.684289 0.729211i $$-0.739887\pi$$
0.973660 + 0.228006i $$0.0732205\pi$$
$$228$$ 0 0
$$229$$ 1383.67 + 2396.59i 0.399282 + 0.691577i 0.993638 0.112625i $$-0.0359260\pi$$
−0.594355 + 0.804203i $$0.702593\pi$$
$$230$$ 900.560 0.258179
$$231$$ 0 0
$$232$$ −1328.00 −0.375808
$$233$$ −3245.00 5620.50i −0.912391 1.58031i −0.810677 0.585493i $$-0.800901\pi$$
−0.101713 0.994814i $$-0.532432\pi$$
$$234$$ 0 0
$$235$$ −968.000 + 1676.63i −0.268704 + 0.465408i
$$236$$ 1332.08 + 2307.23i 0.367419 + 0.636388i
$$237$$ 0 0
$$238$$ 0 0
$$239$$ 4296.00 1.16270 0.581350 0.813654i $$-0.302525\pi$$
0.581350 + 0.813654i $$0.302525\pi$$
$$240$$ 0 0
$$241$$ 2260.78 3915.79i 0.604272 1.04663i −0.387894 0.921704i $$-0.626797\pi$$
0.992166 0.124926i $$-0.0398695\pi$$
$$242$$ −931.000 + 1612.54i −0.247301 + 0.428339i
$$243$$ 0 0
$$244$$ −1088.18 −0.285506
$$245$$ 0 0
$$246$$ 0 0
$$247$$ −308.000 533.472i −0.0793424 0.137425i
$$248$$ 825.513 1429.83i 0.211372 0.366106i
$$249$$ 0 0
$$250$$ −1519.69 2632.19i −0.384456 0.665897i
$$251$$ 5581.59 1.40361 0.701807 0.712367i $$-0.252377\pi$$
0.701807 + 0.712367i $$0.252377\pi$$
$$252$$ 0 0
$$253$$ 960.000 0.238556
$$254$$ 2312.00 + 4004.50i 0.571133 + 0.989231i
$$255$$ 0 0
$$256$$ −128.000 + 221.703i −0.0312500 + 0.0541266i
$$257$$ 750.467 + 1299.85i 0.182151 + 0.315495i 0.942613 0.333888i $$-0.108361\pi$$
−0.760462 + 0.649383i $$0.775027\pi$$
$$258$$ 0 0
$$259$$ 0 0
$$260$$ −2464.00 −0.587734
$$261$$ 0 0
$$262$$ −253.282 + 438.698i −0.0597246 + 0.103446i
$$263$$ −200.000 + 346.410i −0.0468917 + 0.0812189i −0.888519 0.458841i $$-0.848265\pi$$
0.841627 + 0.540059i $$0.181598\pi$$
$$264$$ 0 0
$$265$$ −581.612 −0.134823
$$266$$ 0 0
$$267$$ 0 0
$$268$$ −1160.00 2009.18i −0.264397 0.457948i
$$269$$ 136.022 235.597i 0.0308305 0.0534000i −0.850198 0.526462i $$-0.823518\pi$$
0.881029 + 0.473062i $$0.156851\pi$$
$$270$$ 0 0
$$271$$ 3452.15 + 5979.29i 0.773812 + 1.34028i 0.935460 + 0.353433i $$0.114986\pi$$
−0.161648 + 0.986848i $$0.551681\pi$$
$$272$$ 900.560 0.200752
$$273$$ 0 0
$$274$$ −2228.00 −0.491235
$$275$$ −370.000 640.859i −0.0811340 0.140528i
$$276$$ 0 0
$$277$$ 3385.00 5862.99i 0.734242 1.27174i −0.220814 0.975316i $$-0.570871\pi$$
0.955055 0.296428i $$-0.0957954\pi$$
$$278$$ −1378.98 2388.47i −0.297503 0.515290i
$$279$$ 0 0
$$280$$ 0 0
$$281$$ −1878.00 −0.398691 −0.199345 0.979929i $$-0.563882\pi$$
−0.199345 + 0.979929i $$0.563882\pi$$
$$282$$ 0 0
$$283$$ 192.307 333.086i 0.0403939 0.0699642i −0.845122 0.534574i $$-0.820472\pi$$
0.885516 + 0.464610i $$0.153805\pi$$
$$284$$ −1088.00 + 1884.47i −0.227327 + 0.393742i
$$285$$ 0 0
$$286$$ −2626.63 −0.543063
$$287$$ 0 0
$$288$$ 0 0
$$289$$ 872.500 + 1511.21i 0.177590 + 0.307595i
$$290$$ 1557.22 2697.18i 0.315321 0.546151i
$$291$$ 0 0
$$292$$ −1200.75 2079.75i −0.240645 0.416810i
$$293$$ −3742.95 −0.746299 −0.373149 0.927771i $$-0.621722\pi$$
−0.373149 + 0.927771i $$0.621722\pi$$
$$294$$ 0 0
$$295$$ −6248.00 −1.23313
$$296$$ −312.000 540.400i −0.0612656 0.106115i
$$297$$ 0 0
$$298$$ 946.000 1638.52i 0.183894 0.318513i
$$299$$ −1575.98 2729.68i −0.304820 0.527964i
$$300$$ 0 0
$$301$$ 0 0
$$302$$ −1664.00 −0.317061
$$303$$ 0 0
$$304$$ 75.0467 129.985i 0.0141586 0.0245235i
$$305$$ 1276.00 2210.10i 0.239553 0.414917i
$$306$$ 0 0
$$307$$ −722.324 −0.134284 −0.0671420 0.997743i $$-0.521388\pi$$
−0.0671420 + 0.997743i $$0.521388\pi$$
$$308$$ 0 0
$$309$$ 0 0
$$310$$ 1936.00 + 3353.25i 0.354701 + 0.614361i
$$311$$ −3639.76 + 6304.25i −0.663640 + 1.14946i 0.316012 + 0.948755i $$0.397656\pi$$
−0.979652 + 0.200703i $$0.935677\pi$$
$$312$$ 0 0
$$313$$ 759.847 + 1316.09i 0.137218 + 0.237668i 0.926442 0.376437i $$-0.122851\pi$$
−0.789225 + 0.614104i $$0.789517\pi$$
$$314$$ 5759.83 1.03518
$$315$$ 0 0
$$316$$ −2720.00 −0.484215
$$317$$ 1179.00 + 2042.09i 0.208893 + 0.361814i 0.951366 0.308062i $$-0.0996805\pi$$
−0.742473 + 0.669876i $$0.766347\pi$$
$$318$$ 0 0
$$319$$ 1660.00 2875.20i 0.291355 0.504641i
$$320$$ −300.187 519.938i −0.0524404 0.0908295i
$$321$$ 0 0
$$322$$ 0 0
$$323$$ −528.000 −0.0909557
$$324$$ 0 0
$$325$$ −1214.82 + 2104.13i −0.207341 + 0.359126i
$$326$$ 636.000 1101.58i 0.108051 0.187151i
$$327$$ 0 0
$$328$$ −3151.96 −0.530603
$$329$$ 0 0
$$330$$ 0 0
$$331$$ −1186.00 2054.21i −0.196944 0.341117i 0.750592 0.660766i $$-0.229768\pi$$
−0.947536 + 0.319649i $$0.896435\pi$$
$$332$$ −393.995 + 682.419i −0.0651304 + 0.112809i
$$333$$ 0 0
$$334$$ −656.658 1137.37i −0.107577 0.186329i
$$335$$ 5440.88 0.887365
$$336$$ 0 0
$$337$$ −250.000 −0.0404106 −0.0202053 0.999796i $$-0.506432\pi$$
−0.0202053 + 0.999796i $$0.506432\pi$$
$$338$$ 2115.00 + 3663.29i 0.340357 + 0.589516i
$$339$$ 0 0
$$340$$ −1056.00 + 1829.05i −0.168440 + 0.291747i
$$341$$ 2063.78 + 3574.58i 0.327742 + 0.567666i
$$342$$ 0 0
$$343$$ 0 0
$$344$$ −3488.00 −0.546687
$$345$$ 0 0
$$346$$ 666.039 1153.61i 0.103487 0.179245i
$$347$$ 4770.00 8261.88i 0.737945 1.27816i −0.215474 0.976510i $$-0.569130\pi$$
0.953419 0.301649i $$-0.0975371\pi$$
$$348$$ 0 0
$$349$$ 5712.93 0.876235 0.438117 0.898918i $$-0.355645\pi$$
0.438117 + 0.898918i $$0.355645\pi$$
$$350$$ 0 0
$$351$$ 0 0
$$352$$ −320.000 554.256i −0.0484547 0.0839260i
$$353$$ −2195.11 + 3802.05i −0.330975 + 0.573265i −0.982703 0.185187i $$-0.940711\pi$$
0.651728 + 0.758452i $$0.274044\pi$$
$$354$$ 0 0
$$355$$ −2551.59 4419.48i −0.381476 0.660737i
$$356$$ −6003.73 −0.893812
$$357$$ 0 0
$$358$$ −6456.00 −0.953101
$$359$$ 920.000 + 1593.49i 0.135253 + 0.234265i 0.925694 0.378273i $$-0.123482\pi$$
−0.790441 + 0.612538i $$0.790149\pi$$
$$360$$ 0 0
$$361$$ 3385.50 5863.86i 0.493585 0.854914i
$$362$$ 2823.63 + 4890.67i 0.409963 + 0.710077i
$$363$$ 0 0
$$364$$ 0 0
$$365$$ 5632.00 0.807650
$$366$$ 0 0
$$367$$ −1482.17 + 2567.20i −0.210814 + 0.365140i −0.951969 0.306193i $$-0.900945\pi$$
0.741156 + 0.671333i $$0.234278\pi$$
$$368$$ 384.000 665.108i 0.0543951 0.0942150i
$$369$$ 0 0
$$370$$ 1463.41 0.205619
$$371$$ 0 0
$$372$$ 0 0
$$373$$ −1991.00 3448.51i −0.276381 0.478706i 0.694102 0.719877i $$-0.255802\pi$$
−0.970483 + 0.241171i $$0.922468\pi$$
$$374$$ −1125.70 + 1949.77i −0.155638 + 0.269573i
$$375$$ 0 0
$$376$$ 825.513 + 1429.83i 0.113225 + 0.196111i
$$377$$ −10900.5 −1.48914
$$378$$ 0 0
$$379$$ 2676.00 0.362683 0.181342 0.983420i $$-0.441956\pi$$
0.181342 + 0.983420i $$0.441956\pi$$
$$380$$ 176.000 + 304.841i 0.0237595 + 0.0411527i
$$381$$ 0 0
$$382$$ 2136.00 3699.66i 0.286092 0.495526i
$$383$$ −3517.81 6093.03i −0.469326 0.812896i 0.530059 0.847961i $$-0.322170\pi$$
−0.999385 + 0.0350645i $$0.988836\pi$$
$$384$$ 0 0
$$385$$ 0 0
$$386$$ −3316.00 −0.437254
$$387$$ 0 0
$$388$$ −1313.32 + 2274.73i −0.171839 + 0.297634i
$$389$$ 4329.00 7498.05i 0.564239 0.977291i −0.432881 0.901451i $$-0.642503\pi$$
0.997120 0.0758397i $$-0.0241637\pi$$
$$390$$ 0 0
$$391$$ −2701.68 −0.349437
$$392$$ 0 0
$$393$$ 0 0
$$394$$ 978.000 + 1693.95i 0.125053 + 0.216598i
$$395$$ 3189.48 5524.35i 0.406279 0.703696i
$$396$$ 0 0
$$397$$ −4526.25 7839.70i −0.572207 0.991091i −0.996339 0.0854907i $$-0.972754\pi$$
0.424132 0.905600i $$-0.360579\pi$$
$$398$$ −9868.63 −1.24289
$$399$$ 0 0
$$400$$ −592.000 −0.0740000
$$401$$ −2853.00 4941.54i −0.355292 0.615383i 0.631876 0.775069i $$-0.282285\pi$$
−0.987168 + 0.159686i $$0.948952\pi$$
$$402$$ 0 0
$$403$$ 6776.00 11736.4i 0.837560 1.45070i
$$404$$ −243.902 422.450i −0.0300360 0.0520239i
$$405$$ 0 0
$$406$$ 0 0
$$407$$ 1560.00 0.189991
$$408$$ 0 0
$$409$$ 1210.13 2096.00i 0.146301 0.253400i −0.783557 0.621320i $$-0.786597\pi$$
0.929857 + 0.367920i $$0.119930\pi$$
$$410$$ 3696.00 6401.66i 0.445201 0.771111i
$$411$$ 0 0
$$412$$ 5478.41 0.655101
$$413$$ 0 0
$$414$$ 0 0
$$415$$ −924.000 1600.41i −0.109295 0.189304i
$$416$$ −1050.65 + 1819.78i −0.123828 + 0.214477i
$$417$$ 0 0
$$418$$ 187.617 + 324.962i 0.0219537 + 0.0380249i
$$419$$ −1510.31 −0.176095 −0.0880473 0.996116i $$-0.528063\pi$$
−0.0880473 + 0.996116i $$0.528063\pi$$
$$420$$ 0 0
$$421$$ −16770.0 −1.94138 −0.970689 0.240341i $$-0.922741\pi$$
−0.970689 + 0.240341i $$0.922741\pi$$
$$422$$ 1556.00 + 2695.07i 0.179490 + 0.310886i
$$423$$ 0 0
$$424$$ −248.000 + 429.549i −0.0284055 + 0.0491998i
$$425$$ 1041.27 + 1803.54i 0.118845 + 0.205846i
$$426$$ 0 0
$$427$$ 0 0
$$428$$ 1040.00 0.117454
$$429$$ 0 0
$$430$$ 4090.04 7084.16i 0.458696 0.794485i
$$431$$ 668.000 1157.01i 0.0746553 0.129307i −0.826281 0.563258i $$-0.809548\pi$$
0.900936 + 0.433951i $$0.142881\pi$$
$$432$$ 0 0
$$433$$ 11163.2 1.23896 0.619479 0.785013i $$-0.287344\pi$$
0.619479 + 0.785013i $$0.287344\pi$$
$$434$$ 0 0
$$435$$ 0 0
$$436$$ −3764.00 6519.44i −0.413447 0.716111i
$$437$$ −225.140 + 389.954i −0.0246451 + 0.0426865i
$$438$$ 0 0
$$439$$ −1801.12 3119.63i −0.195815 0.339161i 0.751352 0.659901i $$-0.229402\pi$$
−0.947167 + 0.320740i $$0.896069\pi$$
$$440$$ 1500.93 0.162623
$$441$$ 0 0
$$442$$ 7392.00 0.795479
$$443$$ 3174.00 + 5497.53i 0.340409 + 0.589606i 0.984509 0.175336i $$-0.0561011\pi$$
−0.644099 + 0.764942i $$0.722768\pi$$
$$444$$ 0 0
$$445$$ 7040.00 12193.6i 0.749951 1.29895i
$$446$$ −2889.30 5004.41i −0.306754 0.531313i
$$447$$ 0 0
$$448$$ 0 0
$$449$$ −7170.00 −0.753615 −0.376808 0.926292i $$-0.622978\pi$$
−0.376808 + 0.926292i $$0.622978\pi$$
$$450$$ 0 0
$$451$$ 3939.95 6824.19i 0.411364 0.712503i
$$452$$ −2572.00 + 4454.83i −0.267648 + 0.463579i
$$453$$ 0 0
$$454$$ 3958.71 0.409232
$$455$$ 0 0
$$456$$ 0 0
$$457$$ −3433.00 5946.13i −0.351398 0.608639i 0.635097 0.772433i $$-0.280960\pi$$
−0.986495 + 0.163793i $$0.947627\pi$$
$$458$$ −2767.35 + 4793.18i −0.282335 + 0.489019i
$$459$$ 0 0
$$460$$ 900.560 + 1559.82i 0.0912800 + 0.158102i
$$461$$ 1378.98 0.139318 0.0696590 0.997571i $$-0.477809\pi$$
0.0696590 + 0.997571i $$0.477809\pi$$
$$462$$ 0 0
$$463$$ 2648.00 0.265795 0.132897 0.991130i $$-0.457572\pi$$
0.132897 + 0.991130i $$0.457572\pi$$
$$464$$ −1328.00 2300.16i −0.132868 0.230135i
$$465$$ 0 0
$$466$$ 6490.00 11241.0i 0.645158 1.11745i
$$467$$ 6167.90 + 10683.1i 0.611170 + 1.05858i 0.991044 + 0.133539i $$0.0426340\pi$$
−0.379874 + 0.925038i $$0.624033\pi$$
$$468$$ 0 0
$$469$$ 0 0
$$470$$ −3872.00 −0.380004
$$471$$ 0 0
$$472$$ −2664.16 + 4614.45i −0.259805 + 0.449995i
$$473$$ 4360.00 7551.74i 0.423833 0.734100i
$$474$$ 0 0
$$475$$ 347.091 0.0335276
$$476$$ 0 0
$$477$$ 0 0
$$478$$ 4296.00 + 7440.89i 0.411076 + 0.712005i
$$479$$ 6669.77 11552.4i 0.636221 1.10197i −0.350035 0.936737i $$-0.613830\pi$$
0.986255 0.165229i $$-0.0528365\pi$$
$$480$$ 0 0
$$481$$ −2560.97 4435.72i −0.242765 0.420482i
$$482$$ 9043.12 0.854570
$$483$$ 0 0
$$484$$ −3724.00 −0.349737
$$485$$ −3080.00 5334.72i −0.288362 0.499458i
$$486$$ 0 0
$$487$$ −6968.00 + 12068.9i −0.648358 + 1.12299i 0.335157 + 0.942162i $$0.391211\pi$$
−0.983515 + 0.180826i $$0.942123\pi$$
$$488$$ −1088.18 1884.78i −0.100941 0.174836i
$$489$$ 0 0
$$490$$ 0 0
$$491$$ 12276.0 1.12833 0.564163 0.825663i $$-0.309199\pi$$
0.564163 + 0.825663i $$0.309199\pi$$
$$492$$ 0 0
$$493$$ −4671.65 + 8091.54i −0.426776 + 0.739198i
$$494$$ 616.000 1066.94i 0.0561035 0.0971742i
$$495$$ 0 0
$$496$$ 3302.05 0.298924
$$497$$ 0 0
$$498$$ 0 0
$$499$$ 1110.00 + 1922.58i 0.0995800 + 0.172478i 0.911511 0.411276i $$-0.134917\pi$$
−0.811931 + 0.583754i $$0.801583\pi$$
$$500$$ 3039.39 5264.38i 0.271851 0.470860i
$$501$$ 0 0
$$502$$ 5581.59 + 9667.61i 0.496253 + 0.859535i
$$503$$ −11294.5 −1.00119 −0.500594 0.865682i $$-0.666885\pi$$
−0.500594 + 0.865682i $$0.666885\pi$$
$$504$$ 0 0
$$505$$ 1144.00 0.100807
$$506$$ 960.000 + 1662.77i 0.0843423 + 0.146085i
$$507$$ 0 0
$$508$$ −4624.00 + 8009.00i −0.403852 + 0.699492i
$$509$$ 7940.87 + 13754.0i 0.691499 + 1.19771i 0.971347 + 0.237667i $$0.0763827\pi$$
−0.279848 + 0.960044i $$0.590284\pi$$
$$510$$ 0 0
$$511$$ 0 0
$$512$$ −512.000 −0.0441942
$$513$$ 0 0
$$514$$ −1500.93 + 2599.69i −0.128800 + 0.223089i
$$515$$ −6424.00 + 11126.7i −0.549661 + 0.952040i
$$516$$ 0 0
$$517$$ −4127.57 −0.351122
$$518$$ 0 0
$$519$$ 0 0
$$520$$ −2464.00 4267.77i −0.207795 0.359912i
$$521$$ −5806.73 + 10057.6i −0.488287 + 0.845738i −0.999909 0.0134723i $$-0.995712\pi$$
0.511622 + 0.859211i $$0.329045\pi$$
$$522$$ 0 0
$$523$$ 6308.61 + 10926.8i 0.527450 + 0.913570i 0.999488 + 0.0319918i $$0.0101850\pi$$
−0.472038 + 0.881578i $$0.656482\pi$$
$$524$$ −1013.13 −0.0844633
$$525$$ 0 0
$$526$$ −800.000 −0.0663149
$$527$$ −5808.00 10059.8i −0.480077 0.831517i
$$528$$ 0 0
$$529$$ 4931.50 8541.61i 0.405318 0.702031i
$$530$$ −581.612 1007.38i −0.0476672 0.0825619i
$$531$$ 0 0
$$532$$ 0 0
$$533$$ −25872.0 −2.10252
$$534$$ 0 0
$$535$$ −1219.51 + 2112.25i −0.0985494 + 0.170693i
$$536$$ 2320.00 4018.36i 0.186957 0.323818i
$$537$$ 0 0
$$538$$ 544.088 0.0436009
$$539$$ 0 0
$$540$$ 0 0
$$541$$ −899.000 1557.11i −0.0714437 0.123744i 0.828091 0.560594i $$-0.189427\pi$$
−0.899534 + 0.436850i $$0.856094\pi$$
$$542$$ −6904.29 + 11958.6i −0.547167 + 0.947722i
$$543$$ 0 0
$$544$$ 900.560 + 1559.82i 0.0709764 + 0.122935i
$$545$$ 17654.7 1.38761
$$546$$ 0 0
$$547$$ 1276.00 0.0997401 0.0498700 0.998756i $$-0.484119\pi$$
0.0498700 + 0.998756i $$0.484119\pi$$
$$548$$ −2228.00 3859.01i −0.173678 0.300819i
$$549$$ 0 0
$$550$$ 740.000 1281.72i 0.0573704 0.0993684i
$$551$$ 778.609 + 1348.59i 0.0601994 + 0.104268i
$$552$$ 0 0
$$553$$ 0 0
$$554$$ 13540.0 1.03837
$$555$$ 0 0
$$556$$ 2757.96 4776.93i 0.210366 0.364365i
$$557$$ 1347.00 2333.07i 0.102467 0.177478i −0.810233 0.586107i $$-0.800660\pi$$
0.912701 + 0.408629i $$0.133993\pi$$
$$558$$ 0 0
$$559$$ −28630.3 −2.16625
$$560$$ 0 0
$$561$$ 0 0
$$562$$ −1878.00 3252.79i −0.140958 0.244147i
$$563$$ 7884.59 13656.5i 0.590223 1.02230i −0.403979 0.914768i $$-0.632373\pi$$
0.994202 0.107529i $$-0.0342937\pi$$
$$564$$ 0 0
$$565$$ −6031.87 10447.5i −0.449138 0.777930i
$$566$$ 769.228 0.0571256
$$567$$ 0 0
$$568$$ −4352.00 −0.321489
$$569$$ 6303.00 + 10917.1i 0.464386 + 0.804340i 0.999174 0.0406466i $$-0.0129418\pi$$
−0.534788 + 0.844986i $$0.679608\pi$$
$$570$$ 0 0
$$571$$ −3426.00 + 5934.01i −0.251092 + 0.434904i −0.963827 0.266529i $$-0.914123\pi$$
0.712735 + 0.701434i $$0.247456\pi$$
$$572$$ −2626.63 4549.46i −0.192002 0.332557i
$$573$$ 0 0
$$574$$ 0 0
$$575$$ 1776.00 0.128808
$$576$$ 0 0
$$577$$ 7185.72 12446.0i 0.518449 0.897981i −0.481321 0.876545i $$-0.659843\pi$$
0.999770 0.0214362i $$-0.00682388\pi$$
$$578$$ −1745.00 + 3022.43i −0.125575 + 0.217503i
$$579$$ 0 0
$$580$$ 6228.87 0.445931
$$581$$ 0 0
$$582$$ 0 0
$$583$$ −620.000 1073.87i −0.0440442 0.0762868i
$$584$$ 2401.49 4159.51i 0.170162 0.294729i
$$585$$ 0 0
$$586$$ −3742.95 6482.98i −0.263857 0.457013i
$$587$$ 18977.4 1.33438 0.667191 0.744887i $$-0.267497\pi$$
0.667191 + 0.744887i $$0.267497\pi$$
$$588$$ 0 0
$$589$$ −1936.00 −0.135435
$$590$$ −6248.00 10821.9i −0.435976 0.755133i
$$591$$ 0 0
$$592$$ 624.000 1080.80i 0.0433214 0.0750348i
$$593$$ −4108.80 7116.66i −0.284534 0.492826i 0.687962 0.725746i $$-0.258505\pi$$
−0.972496 + 0.232920i $$0.925172\pi$$
$$594$$ 0 0
$$595$$ 0 0
$$596$$ 3784.00 0.260065
$$597$$ 0 0
$$598$$ 3151.96 5459.35i 0.215540 0.373327i
$$599$$ −9552.00 + 16544.5i −0.651559 + 1.12853i 0.331185 + 0.943566i $$0.392552\pi$$
−0.982744 + 0.184968i $$0.940782\pi$$
$$600$$ 0 0
$$601$$ −21538.4 −1.46185 −0.730923 0.682460i $$-0.760910\pi$$
−0.730923 + 0.682460i $$0.760910\pi$$
$$602$$ 0 0
$$603$$ 0 0
$$604$$ −1664.00 2882.13i −0.112098 0.194159i
$$605$$ 4366.78 7563.48i 0.293446 0.508263i
$$606$$ 0 0
$$607$$ 6866.77 + 11893.6i 0.459166 + 0.795298i 0.998917 0.0465262i $$-0.0148151\pi$$
−0.539751 + 0.841824i $$0.681482\pi$$
$$608$$ 300.187 0.0200233
$$609$$ 0 0
$$610$$ 5104.00 0.338779
$$611$$ 6776.00 + 11736.4i 0.448654 + 0.777092i
$$612$$ 0 0
$$613$$ −14017.0 + 24278.2i −0.923558 + 1.59965i −0.129695 + 0.991554i $$0.541400\pi$$
−0.793863 + 0.608096i $$0.791934\pi$$
$$614$$ −722.324 1251.10i −0.0474766 0.0822319i
$$615$$ 0 0
$$616$$ 0 0
$$617$$ 8258.00 0.538824 0.269412 0.963025i $$-0.413171\pi$$
0.269412 + 0.963025i $$0.413171\pi$$
$$618$$ 0 0
$$619$$ −2565.66 + 4443.85i −0.166595 + 0.288551i −0.937221 0.348737i $$-0.886611\pi$$
0.770625 + 0.637288i $$0.219944\pi$$
$$620$$ −3872.00 + 6706.50i −0.250812 + 0.434419i
$$621$$ 0 0
$$622$$ −14559.1 −0.938529
$$623$$ 0 0
$$624$$ 0 0
$$625$$ 4815.50 + 8340.69i 0.308192 + 0.533804i
$$626$$ −1519.69 + 2632.19i −0.0970275 + 0.168057i
$$627$$ 0 0
$$628$$ 5759.83 + 9976.32i 0.365991 + 0.633915i
$$629$$ −4390.23 −0.278299
$$630$$ 0 0
$$631$$ 912.000 0.0575375 0.0287687 0.999586i $$-0.490841\pi$$
0.0287687 + 0.999586i $$0.490841\pi$$
$$632$$ −2720.00 4711.18i −0.171196 0.296520i
$$633$$ 0 0
$$634$$ −2358.00 + 4084.18i −0.147710 + 0.255841i
$$635$$ −10844.2 18782.8i −0.677702 1.17381i
$$636$$ 0 0
$$637$$ 0 0
$$638$$ 6640.00 0.412038
$$639$$ 0 0
$$640$$ 600.373 1039.88i 0.0370810 0.0642262i
$$641$$ −445.000 + 770.763i −0.0274203 + 0.0474934i −0.879410 0.476065i $$-0.842063\pi$$
0.851990 + 0.523559i $$0.175396\pi$$
$$642$$ 0 0
$$643$$ 29352.6 1.80024 0.900120 0.435642i $$-0.143479\pi$$
0.900120 + 0.435642i $$0.143479\pi$$
$$644$$ 0 0
$$645$$ 0 0
$$646$$ −528.000 914.523i −0.0321577 0.0556988i
$$647$$ −5938.07 + 10285.0i −0.360818 + 0.624956i −0.988096 0.153840i $$-0.950836\pi$$
0.627277 + 0.778796i $$0.284169\pi$$
$$648$$ 0 0
$$649$$ −6660.39 11536.1i −0.402840 0.697739i
$$650$$ −4859.27 −0.293225
$$651$$ 0 0
$$652$$ 2544.00 0.152808
$$653$$ −10763.0 18642.1i −0.645006 1.11718i −0.984300 0.176502i $$-0.943522\pi$$
0.339294 0.940680i $$-0.389812\pi$$
$$654$$ 0 0
$$655$$ 1188.00 2057.68i 0.0708687 0.122748i
$$656$$ −3151.96 5459.35i −0.187597 0.324927i
$$657$$ 0 0
$$658$$ 0 0
$$659$$ −23452.0 −1.38628 −0.693141 0.720802i $$-0.743774\pi$$
−0.693141 + 0.720802i $$0.743774\pi$$
$$660$$ 0 0
$$661$$ −13334.9 + 23096.6i −0.784668 + 1.35909i 0.144529 + 0.989501i $$0.453833\pi$$
−0.929197 + 0.369584i $$0.879500\pi$$
$$662$$ 2372.00 4108.42i 0.139260 0.241206i
$$663$$ 0 0
$$664$$ −1575.98 −0.0921082
$$665$$ 0 0
$$666$$ 0 0
$$667$$ 3984.00 + 6900.49i 0.231276 + 0.400582i
$$668$$ 1313.32 2274.73i 0.0760685 0.131754i
$$669$$ 0 0
$$670$$ 5440.88 + 9423.88i 0.313731 + 0.543398i
$$671$$ 5440.88 0.313030
$$672$$ 0 0
$$673$$ −13858.0 −0.793739 −0.396870 0.917875i $$-0.629904\pi$$
−0.396870 + 0.917875i $$0.629904\pi$$
$$674$$ −250.000 433.013i −0.0142873 0.0247463i
$$675$$ 0 0
$$676$$ −4230.00 + 7326.57i −0.240669 + 0.416851i
$$677$$ −16224.1 28101.0i −0.921041 1.59529i −0.797808 0.602912i $$-0.794007\pi$$
−0.123233 0.992378i $$-0.539326\pi$$
$$678$$ 0 0
$$679$$ 0 0
$$680$$ −4224.00 −0.238210
$$681$$ 0 0
$$682$$ −4127.57 + 7149.15i −0.231749 + 0.401401i
$$683$$ −13906.0 + 24085.9i −0.779060 + 1.34937i 0.153423 + 0.988161i $$0.450970\pi$$
−0.932484 + 0.361212i $$0.882363\pi$$
$$684$$ 0 0
$$685$$ 10450.2 0.582895
$$686$$ 0 0
$$687$$ 0 0
$$688$$ −3488.00 6041.39i −0.193283 0.334776i
$$689$$ −2035.64 + 3525.83i −0.112557 + 0.194954i
$$690$$ 0 0
$$691$$ −651.968 1129.24i −0.0358929 0.0621684i 0.847521 0.530762i $$-0.178094\pi$$
−0.883414 + 0.468594i $$0.844761\pi$$
$$692$$ 2664.16 0.146353
$$693$$ 0 0
$$694$$ 19080.0 1.04361
$$695$$ 6468.00 + 11202.9i 0.353015 + 0.611439i
$$696$$ 0 0
$$697$$ −11088.0 + 19205.0i −0.602565 + 1.04367i
$$698$$ 5712.93 + 9895.08i 0.309796 + 0.536582i
$$699$$ 0 0
$$700$$ 0 0
$$701$$ −22906.0 −1.23416 −0.617081 0.786900i $$-0.711685\pi$$
−0.617081 + 0.786900i $$0.711685\pi$$
$$702$$ 0 0
$$703$$ −365.852 + 633.675i −0.0196279 + 0.0339965i
$$704$$ 640.000 1108.51i 0.0342627 0.0593447i
$$705$$ 0 0
$$706$$ −8780.46 −0.468069
$$707$$ 0 0
$$708$$ 0 0
$$709$$ 7543.00 + 13064.9i 0.399553 + 0.692047i 0.993671 0.112332i $$-0.0358319\pi$$
−0.594117 + 0.804378i $$0.702499\pi$$
$$710$$ 5103.17 8838.95i 0.269745 0.467211i
$$711$$ 0 0
$$712$$ −6003.73 10398.8i −0.316010 0.547346i
$$713$$ −9906.16 −0.520321
$$714$$ 0 0
$$715$$ 12320.0 0.644394
$$716$$ −6456.00 11182.1i −0.336972 0.583653i
$$717$$ 0 0
$$718$$ −1840.00 + 3186.97i −0.0956381 + 0.165650i
$$719$$ 10272.0 + 17791.6i 0.532797 + 0.922832i 0.999266 + 0.0382947i $$0.0121926\pi$$
−0.466469 + 0.884538i $$0.654474\pi$$
$$720$$ 0 0
$$721$$ 0 0
$$722$$ 13542.0 0.698035
$$723$$ 0 0
$$724$$ −5647.26 + 9781.34i −0.289888 + 0.502100i
$$725$$ 3071.00 5319.13i 0.157316 0.272479i
$$726$$ 0 0
$$727$$ 7223.24 0.368494 0.184247 0.982880i $$-0.441015\pi$$
0.184247 + 0.982880i $$0.441015\pi$$
$$728$$ 0 0
$$729$$ 0 0
$$730$$ 5632.00 + 9754.91i 0.285547 + 0.494583i
$$731$$ −12270.1 + 21252.5i −0.620830 + 1.07531i
$$732$$ 0 0
$$733$$ 14713.8 + 25485.1i 0.741430 + 1.28419i 0.951844 + 0.306581i $$0.0991852\pi$$
−0.210415 + 0.977612i $$0.567481\pi$$
$$734$$ −5928.69 −0.298136
$$735$$ 0 0
$$736$$ 1536.00 0.0769262
$$737$$ 5800.00 + 10045.9i 0.289886 + 0.502097i
$$738$$ 0 0
$$739$$ −16334.0 + 28291.3i −0.813066 + 1.40827i 0.0976420 + 0.995222i $$0.468870\pi$$
−0.910708 + 0.413050i $$0.864463\pi$$
$$740$$ 1463.41 + 2534.70i 0.0726973 + 0.125915i
$$741$$ 0 0
$$742$$ 0 0
$$743$$ 37056.0 1.82968 0.914840 0.403816i $$-0.132316\pi$$
0.914840 + 0.403816i $$0.132316\pi$$
$$744$$ 0 0
$$745$$ −4437.13 + 7685.34i −0.218207 + 0.377945i
$$746$$ 3982.00 6897.03i 0.195431 0.338496i
$$747$$ 0 0
$$748$$ −4502.80 −0.220105
$$749$$ 0 0
$$750$$ 0 0
$$751$$ 9804.00 + 16981.0i 0.476369 + 0.825095i 0.999633 0.0270752i $$-0.00861935\pi$$
−0.523265 + 0.852170i $$0.675286\pi$$
$$752$$ −1651.03 + 2859.66i −0.0800621 + 0.138672i
$$753$$ 0 0
$$754$$ −10900.5 18880.3i −0.526490 0.911908i
$$755$$ 7804.85 0.376222
$$756$$ 0 0
$$757$$ 19378.0 0.930390 0.465195 0.885208i $$-0.345984\pi$$
0.465195 + 0.885208i $$0.345984\pi$$
$$758$$ 2676.00 + 4634.97i 0.128228 + 0.222097i
$$759$$ 0 0
$$760$$ −352.000 + 609.682i −0.0168005 + 0.0290993i
$$761$$ 6988.72 + 12104.8i 0.332905 + 0.576609i 0.983080 0.183176i $$-0.0586377\pi$$
−0.650175 + 0.759785i $$0.725304\pi$$
$$762$$ 0 0
$$763$$ 0 0
$$764$$ 8544.00 0.404596
$$765$$ 0 0
$$766$$ 7035.62 12186.1i 0.331863 0.574804i
$$767$$ −21868.0 + 37876.5i −1.02948 + 1.78310i
$$768$$ 0 0
$$769$$ −8536.56 −0.400307 −0.200154 0.979765i $$-0.564144\pi$$
−0.200154 + 0.979765i $$0.564144\pi$$
$$770$$ 0 0
$$771$$ 0 0
$$772$$ −3316.00 5743.48i −0.154593 0.267762i
$$773$$ 14648.2 25371.4i 0.681576 1.18052i −0.292924 0.956136i $$-0.594628\pi$$
0.974500 0.224388i $$-0.0720383\pi$$
$$774$$ 0 0
$$775$$ 3818.00 + 6612.97i 0.176963 + 0.306509i
$$776$$ −5253.27 −0.243017
$$777$$ 0 0
$$778$$ 17316.0 0.797955
$$779$$ 1848.00 + 3200.83i 0.0849955 + 0.147216i
$$780$$ 0 0
$$781$$ 5440.00 9422.36i 0.249243 0.431701i
$$782$$ −2701.68 4679.45i −0.123545 0.213985i
$$783$$ 0 0
$$784$$ 0 0
$$785$$ −27016.0 −1.22833
$$786$$ 0 0
$$787$$ 6890.22 11934.2i 0.312084 0.540545i −0.666730 0.745300i $$-0.732306\pi$$
0.978813 + 0.204755i $$0.0656397\pi$$
$$788$$ −1956.00 + 3387.89i −0.0884259 + 0.153158i
$$789$$ 0 0
$$790$$ 12757.9 0.574566
$$791$$ 0 0